Spin diffusion in Fermi gases

TL;DR

This paper analyzes spin diffusion in a two-component Fermi gas, providing analytical expressions for the diffusion coefficient and relaxation time, highlighting a minimum near the Fermi temperature and connecting to quantum limits and shear viscosity.

Contribution

It introduces a variational approach to analytically compute spin diffusion and relaxation in Fermi gases, incorporating strong correlations via Landau parameters derived from Monte Carlo data.

Findings

Spin diffusion coefficient has a minimum below the Fermi temperature.

Diffusion coefficient approaches the quantum limit in the unitarity regime.

Derived low-temperature shear viscosity from Landau parameters.

Abstract

We examine spin diffusion in a two-component homogeneous Fermi gas in the normal phase. Using a variational approach, analytical results are presented for the spin diffusion coefficient and the related spin relaxation time as a function of temperature and interaction strength. For low temperatures, strong correlation effects are included through the Landau parameters which we extract from Monte Carlo results. We show that the spin diffusion coefficient has a minimum for a temperature somewhat below the Fermi temperature with a value that approaches the quantum limit $\sim\hbar/m$ in the unitarity regime where $m$ is the particle mass. We finally derive a value for the low temperature shear viscosity in the normal phase from the Landau parameters.